Re: Mathematica as a New Approach to Teaching Maths

*To*: mathgroup at smc.vnet.net*Subject*: [mg127465] Re: Mathematica as a New Approach to Teaching Maths*From*: "djmpark" <djmpark at comcast.net>*Date*: Fri, 27 Jul 2012 04:56:35 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <9573433.50612.1343288228908.JavaMail.root@m06>

Thanks for mentioning the Conrad Wolfram Ted Talk. http://www.ted.com/talks/lang/en/conrad_wolfram_teaching_kids_real_math_with _computers.html I think Conrad's talk was correct in the main points, glib about the difficulties, correct about the potential. 1) The first point is that Mathematica is difficult. There is a long learning curve. Therefore students headed for careers with technical content should start learning Mathematica early, long before they have to tackle difficult mathematical material. The students would learn some mathematics as they are learning Mathematica but it is a question as to what subjects should be treated when the main objective is to learn Mathematica. (If the aim is to learn real mathematics John Stillwell's "Numbers and Geometry" might be a good source of material.) 2) The test of having skill with Mathematica is the ability to turn real world problems into Mathematica specifications - one of Conrad's points. I call it flying solo, as opposed to copying someone else's code. 3) Conrad disparages learning math by hand with paper and pencil. I would rather co-opt the paradigm. Don't think of Mathematica as a super graphical calculator, or as a programming language (although it is in part these things) but think of it as a piece of paper on which you are writing your ideas, exploring them and presenting them. It is indeed a magic piece of paper with its active calculation, memory and dynamics - but still a piece of paper. 4) This means that students should also learn how to use the Sectional structure of notebook and discuss their material and its development in Text cells. It means that material will often have to be presented in stages with multiple definitions and derivations, graphical presentations and dynamic presentations. One cannot often present coherent material in a single Manipulate statement with lots of Sliders. 5) I didn't quite follow the example that Conrad presented in place of a test. I'm not certain if the student was just to use the dynamic presentation or if he was to design and implement it. The first might not be especially instructive and the second might be too difficult. In any case, I would say that the tests or homework should be in the form of essay questions using the techniques of the preceding point. If a student writes an essay notebook he has something to keep, refer to in the future, and show off. 6) The analogy of jumping over a chasm is one I presented on MathGroup in 2008. http://forums.wolfram.com/mathgroup/archive/2008/Nov/msg00714.html 7) In general, the entire topic of using Mathematica in education is quite difficult because the capabilities that Mathematica brings are so revolutionary. It is all too easy to be unconsciously mired in old paradigms or to fall into the pit of "computer junk". In some cases full-fledged Applications will be necessary, done in Workbench with documentation and examples or course material. Students must learn how to write routines (and their usage messages), but maybe not every extra routine convenient for some subject matter. Such applications should not put the student into a box but rather provide a set of routines that supplement and extend regular Mathematica. An example might be a set of axioms. in the form of rules or routines that apply the rules, for some field of mathematics. Then a student could do derivations or proofs using the axioms. What better way to become familiar with them using them and seeing them in action. 8) Some things along these lines are in the Presentations Application. One of the things students have most difficulty with is custom graphics because the WRI paradigm is really convoluted when it comes to combining things or making geometrical diagrams. Presentations tries to fix that. There is a section on single variable integrals that allows a student to do various manipulations on the integrals such as change of variable, integration by parts or trigonometric substitution so they can see what is happening. There is a Students Linear Equations section that allows matrices to be manipulated with primitive commands and see the results. The matrices also have row and column labels to give them context. I've been working with John Browne's GrassmannAlgebra Application, primarily trying to learn it but also helping with interface and the writing of some introductory examples. This Application would be great for teaching plane geometry because one can easily define points, lines, triangles and other objects algebraically; do things such as calculate lengths, areas and angles; rotate and translate objects; calculate perpendiculars and find intersections; or determine if a point is inside or outside a triangle - all with algebra. One can also draw the geometric diagrams directly using the Grassmann algebra expressions for the coordinates. It's the kind of thing that can be done but it's more than regular Mathematica and it takes development. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: amzoti [mailto:amzoti at gmail.com] Hi All, I just watched what is probably considered a hot button topic issue by some from "Conrad Wolfram's recent TED talk "Stop teaching calculating, start teaching math". I was wondering if any Mathematica users have ever explored this and how they may be approaching it. I love the idea of teaching students to use Mathematica as an exploratory tool which allows them to ask what if questions for learning to problem solve and to ask better questions. Has anyone developed or researched an approach to replace the traditional teaching methods (crank out silly answers) at any level? It would be great if Mathematica could even suggest such as approach! Anyway, would love to hear any feedback, pointers or ideas. Sorry if this is off-topic! Thanks